Question Number 2 and number 3. Make sure to neatly and clearly and mark your an

Question

Question Number 2 and number 3.

Make sure to neatly and clearly and mark your answers. Recall that in Lab 1 we opened a pizzeria and find the profit, P, as a function of the price charged for a pizza, p, was given by P(p) = -5p^2 + 150p - 625. Suppose that you are currently charging $13 per pizza, and you would like to know if it would be beneficial to change the price. In order to determine this, you ask the following questions, What would be the total change profit if price is changed from $13 to $18? Noting that this is an increase of $5 in price, what would be the average change in profit per dollar increase in price? Interpreting P(p) as a function, how would you interpret the previous results graphically? What would be the total change profit if price is changed from $13 to $8? Noting that this is an decrease of $5 in price, what would be the average change in profit per dollar increase in price? Interpreting P(p) as a function, how would you interpret the previous results graphically? Should you change you price to either $8 or $18? Repeat the previous steps for a change in price of $1 per pizza. Instead of looking at the average change in profit with respect to price over some fixed change, imagine you to know the instantaneous rate of change of profit when the price is $13. How would you determine this? What would it be? Based on the instantaneous change in profit with respect to price, would you raise or decrease the price of the pizza?

Explanation / Answer

P(p)= -5p2 + 150p -625

P(13)= -5 (13)2 + 150(13) -625=$480

P(14)= -5 (14)2 + 150(14) -625=$495

Total change in profit= P(14) - P(13)= 495-480=$15

Average change in profit= ( P(14) - P(13) ) / ( 14-13)= $15

Instantaneous change in profit= d/dp -5p2 + 150p -625

= -10p +150

when p=$13

-130+50= $20

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